Question

for an AP the first term is 10, the nth term is 40 and the sum of first n terms is 150. Find the value of n and the command difference d.

Answer 1

a=10

an=40

Sn=150

Sn=n/2 ( a+an)

Sn=n/2 (10+40)

Sn=n/2(50)

Sn=n(25)

150=25n

25n=150

n=150/25

n=6

an=a+(n-1)d

40=10+(6-1)d

40=10+5d

5d=40-10

5d=30

d=30/5

d=6

Answer 2

Given:

a=10

n th term is 40

a+(n-1)d=40

10+(n-1)d=40

(n-1)d=40-10=30..............(1)

Sn=n/2*[2a+(n-1)d]

150=n/2*[20+30]..............(see1)

=300=n*50

n=300/50

=n=6

a+(n-1)d=40

=a+5d=40

=10+5d=40

=5d=30

=d=30/5

=d=6

The number of term is 6 and difference is 6.

Hope it helps.